Circuit Response
every model has an edge, and the figure carries it
Concept

Emitter follower — where it appears

A stage whose output follows its input at unity gain while presenting a high impedance to the source and a low one to the load. Its output impedance is inductive rather than resistive, so a capacitive load resonates with it and the worst case is in the interior of the source range.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

A follower's output impedance from 1 kΩ of source, bare and with 100 pF on it. computed by solving, not by drawing, on a small-signal follower at 2.0 mA with β = 150 and fT = 560 MHz. At 100 Hz the emitter presents 19.08 Ω against a textbook 1/gₘ + Rₛ/(β+1) of 19.55 Ω — the expression is an upper bound here and at every source resistance on the slider, 2.4% high at this one. What it cannot describe is the frequency axis: the β that divided the source resistance down is itself falling, so the impedance rises, and the reactance at 3 MHz is 4.3 Ω — an inductance of 0.229 µH against Rₛ/ωT = 0.284 µH. With 100 pF hung on the output that impedance peaks at 67.0 Ω at 29.3 MHz, 3.51 times its own low-frequency value: an inductive source and a capacitive load are a resonant circuit, and this one is inside a part whose output impedance is quoted as a single number.

The buffer that is not a buffer

An emitter follower is reached for when something has to be driven without being loaded: unity gain in, high impedance seen, low impedance presented. The last of those is a number with a range, and the range is narrow. At a kilohm of source the emitter presents 19.08 ohms at low frequency and 67 ohms at 29 megahertz, because the current gain that made it small is falling — and the peak is worst in the middle of the slider, so it cannot be avoided by making the source stiffer or softer.

semiconductors · Emitter follower A follower with 1000 pF on it looks like -1182 Ω of negative resistance. computed by solving, not by drawing. The impedance looking into the base of an emitter follower carrying 5.0 mA, with 1000 pF on its emitter. The real part is negative from 1.25 MHz upward and reaches -1182 Ω at 3.40 MHz: the load's reactance multiplied by a complex current gain, with nothing added to the model. A negative resistance is not an oscillator until a reactance cancels, and the base lead supplies it — the total loop reactance passes through zero at a frequency the inductance chooses, and the loop resistance there goes negative above 74.9 nH with 10 Ω of source, which is a few centimetres of wire. A hundred ohms of source raises that to 913 nH: the repair is a resistor in the base, and it works by making the source worse.

The input that pushes back

An emitter follower with a capacitor on its emitter has a negative resistance looking into its base — 1182 ohms of it at 3.4 megahertz for a nanofarad, with nothing added to the model. A negative resistance is not an oscillator until a reactance cancels, and the base lead supplies it: with ten ohms of source the loop goes unstable above 74.9 nanohenries, which is seven centimetres of wire. The repair is the opposite of the instinct — a hundred ohms of source raises the threshold to 913 nanohenries, so the fix for a follower that oscillates is to make the thing driving it worse.

semiconductors · Emitter follower A follower fed through 100 nH has an output resistance of -21.9 Ω. computed by solving, not by drawing. The real part of the impedance looking into the emitter, driven by a current source and read, at every frequency. At direct current it is 5.50 ohms, which is the same rₛ/(β+1) + 1/gₘ the follower's first essay computed. Between 110 MHz and 301 MHz it is negative: rπ and Cπ delay the current the transistor sources into the emitter, and past a quarter of a cycle of delay pushing the emitter up makes the device push it up as well. The dashed curve is the same follower with no inductance between the source and the base, and it never goes below zero — the sign belongs to the wire and the transistor together, and to neither alone.

The resistance that is below zero

An emitter follower's output resistance is 5.5 Ω at direct current and −21.9 Ω at 257 MHz, and the sign is not the transistor's: with an ideal source at the base there is no negative band at all, and a hundred nanohenries of wire between the source and the base produces one from 110 to 301 MHz. A capacitance resonating inside that band is a resonator with loss of the wrong sign, so 4.7 to 100 pF on the emitter oscillates while 1 pF and 470 pF do not — a band of load capacitance with quiet ground on both sides of it.

semiconductors · Emitter follower The resistance that just stabilises it is 17 times smaller than the one that damps it. computed by solving, not by drawing. Two consequences of one base resistor, against how much of it there is, for a follower fed through 100 nH of wire with 47 pF on its emitter. The falling curve is the Q of the worst pole pair, rooted from the determinant so that no frequency grid is involved; the rising one is the output impedance the stage presents at low frequency. Bisecting on the SIGN of the pole's real part returns 69.7 Ω — at which the pair is stable with a Q of 1.7e+15, which is to say no damping and a peak whose height belongs to the arithmetic. A Q of one needs 1.15 kΩ, 16.6 times more, and that resistor takes the output impedance from 5.66 to 13.10 Ω — exactly R/(β+1) added, which is the bare follower's own expression with the base resistance in the place of the source resistance.

What the cure at the base costs

Bisecting for the smallest base resistor that stops an emitter follower oscillating gives 8 to 79 ohms. That bisection stops at the sign change, so at the value it returns the pole pair sits on the imaginary axis with a real part of 10⁻⁷ per second and a quality factor of 1.7 × 10¹⁵ — stable, and undamped. A quality factor of one needs 1.15 kΩ at 47 pF, sixteen times more, and that resistor takes the output impedance from 5.66 to 13.10 ohms. The other cure the model has always accepted and nothing has ever used is a resistor at the emitter: it reaches the same damping with 5.68 ohms and costs half the signal.

semiconductors · Emitter follower A 1 MHz sine of 1 V into an emitter follower with 1 nF on its emitter and a 2 mA sink: the input falls at up to 6.28 V/µs, the output can fall at only 2.0, and the transistor switches off. Marched, the base driven by a stiff source and the emitter current Is·exp((vᵢₙ − vₒᵤₜ)/Vₜ). The input (dashed) and the output (solid) over the last of four cycles. The input's steepest fall is 2πfA = 6.28 V/µs; the load can be discharged no faster than the sink allows, I/C = 2.00 V/µs. On every falling stretch the base–emitter junction reverse-biases, the emitter current drops below a hundredth of the sink's (dots), and the output falls as a straight line of slope −2.000 V/µs until the input comes back up to meet it. On the rising half the transistor pushes whatever current the capacitor needs and the output follows a Vbe below the input.

The follower that lets go on the way down

An emitter follower can push current into its load without limit and pull it out only through whatever sinks the emitter. Marched as a large-signal circuit — a 2 mA sink, 1 nF on the emitter — a 1 V, 1 MHz sine asks the output to fall at up to 6.28 V/µs, the sink allows 2.00, and on every falling stretch the junction reverse-biases, the emitter current drops below a hundredth of its quiescent value for 57% of the cycle, and the output falls as a straight line of exactly −I/C. The boundary is a slope, 2πfA ≤ I/C: 2.87 V at 100 kHz, 0.309 V at 1 MHz, creeping above the line only as the period approaches the junction's own 12.9 ns. Past it the follower rectifies — its output's average rises 415 mV at 1 V of drive and 1.30 V at 2 V — and with a resistor in place of the sink the fall slows as the output descends, from 2.41 V/µs to 1.99. None of it is visible to the small-signal model the earlier essays used.

semiconductors · Emitter follower

Named alongside it

The objects these essays reach for when they reach for this one.

Output impedanceStabilityCapacitive loadModel rangeNegative resistancePole pairSmall-signal modelTransit frequencyCurrent mirrorDamping ratioDesign tradeoffDynamic resistance

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